Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<iostream>
#include<cstdio>
#define MN 200000
using namespace std;
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int n,T,a[MN+5],f[MN+5],pos[MN+5];
bool Check(int a,int b,int c){return (a<b&&b<c)||(a<b&&c<a)||(b<c&&c<a);}
int main()
{
	n=read();
	for(int i=1;i<=n;++i) pos[a[i]=read()]=i;
	for(int i=n;i;--i)
		if(!T&&i!=n&&pos[i]>pos[i+1]) f[T]=i+1,++T; 
		else if(T)
		{
			int F=f[T-1];
			if(!Check(pos[F],pos[i],pos[i+1])) f[T]=i+1,++T;
		}
	cout<<T<<endl;
	return 0;
}